Existence of closed embedded curves of constant curvature via min-max

Author:

Lorenzo Sarnataro, Douglas Stryker

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Dynamical Systems (math.DS)

journal:

date:

2023-06-07 16:00:00

Abstract

We find conditions under which Almgren-Pitts min-max for the prescribed geodesic curvature functional in a closed oriented Riemannian surface produces a closed embedded curve of constant curvature. In particular, we find a closed embedded curve of any prescribed constant curvature in any metric on $S^2$ with $1/8$-pinched Gaussian curvature.

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